A fraction reduces to 36. If its denominator is 6x^5, what is its numerator?
To reduce a fraction means to divide both the numerator and the denominator by their greatest common divisor. In this case, we need to find the greatest common divisor of the numerator and the denominator in order to reduce the fraction.
Since the fraction reduces to 36, we can write it as:
$\frac{N}{D} = 36$
where $N$ is the numerator and $D$ is the denominator.
We are given that the denominator is $6x^5$, so we have:
$\frac{N}{6x^5} = 36$
To find the numerator $N$, we need to multiply both sides of the equation by the denominator $6x^5$:
$N = 36 \cdot 6x^5$
Simplifying, we get:
$N = \boxed{216x^5}$